An investigation on planar dielectric light collectors for illumination and solar energy applications

In this paper the performances of inhomogeneous dielectric slabs as solar light collectors for both illumination and solar energy applications are analysed.     

Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.     

Group Representation of Relativistic Quantum Crystal Optics

A group representation of radiation propagation in an anisotropic medium is developed. The system of wave equations for electromagnetic potentials, obtained from the Maxwell equations with account for the constitutive equations, has been factorized. It is shown that the linear differential operator of the factorized system is orthogonal in transparent crystals and unitary in gyrotropic ones and is represented through the momentum operator. On the basis of the commutation relations for the components of this operator, the eigenvalue problem has been solved and the expression for the change in the radiant energy in the crystal in the form of spherical waves has been obtained. The dependences of the ray and phase velocities and the polarization vectors of waves on the birefringence anisotropy and gyrotropy as well as on the angular momentum, displacement current, and bound charge determining them have been analyzed. It has been established that in the general case of gyrotropic crystals where the nonreciprocity phenomenon takes place and in magnetoelectrics Maxwell equations are represented in a form similar to the Dirac equations and the electromagnetic radiation is correctly described by means of bispinors and is quantized as fermions.     

变系数(2+1)维Broer-Kaup方程的精确解

利用齐次平衡原则,导出了变系数(2+1)维Broer-Kaup方程的B?cklund变换(BT),并由该BT,求出了(2+1)维Broer-Kaup方程的各种形式的精确解.     

Effects of diamines and their fluorinated groups on the color lightness and preparation of organosoluble aromatic polyimides from 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]‐hexafluoropropane

To investigate the position and amount of the CF₃ group affecting the coloration of polyimides (PIs), we prepared 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]hexafluoropropane ( 2 ) with four CF₃ groups with 2‐chloro‐5‐nitrobenzotrifluoride and 2,2‐bis(4‐hydroxyphenol)hexafluoropropane. A series of soluble and light‐colored fluorinated PIs ( 5 ) were synthesized from 2 and various aromatic dianhydrides ( 3a – 3f ). 5a – 5f had inherent viscosities ranging from 0.80 to 1.19 dL/g and were soluble in amide polar solvents and even in less polar solvents. The glass‐transition temperatures of 5 were 221–265 °C, and the 10% weight‐loss temperatures were above 493 °C. Their films had cutoff wavelengths between 343 and 390 nm, b* values (a yellowness index) ranging from 5 to 41, dielectric constants of 2.68–3.01 (1 MHz), and moisture absorptions of 0.03–0.29 wt %. In a comparison of the PI series 6 – 8 based on 2,2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane, 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]propane, and 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane, we found that the CF₃ group close to the imide group was more effective in lowering the color; this means that CF₃ of 5 , 7 , and 8f was more effective than that of 6c . The color intensity of the four PI series was lowered in the following order: 5 > 7 > 6 > 8 . The PI 5f , synthesized from diamine 2 and 4,4′‐hexafluoroisopropylidenediphthalic anhydride, had six CF₃ groups in a repeated segment, so it exhibited the lightest color among the four series. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 922–938, 2003     

Letter: Differential Invariants of the Kerr Vacuum

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.     

Temperature coefficient of NH chemical shifts of thioamides and amides in relation to structure

NH chemical shift temperature coefficients have been measured in a large series of N-substituted-3-piperidinethiopropionamides in which the NN distances are short but of varied length, as well as in a couple of the corresponding amides and in some simpler amides and thioamides. Geometries are calculated by means of ab initio DFT methods. The N-substituted-3-piperidinethiopropionamides show in most cases strong intramolecular N–HN hydrogen bonds according to IR spectra and ab initio calculations. For compounds with rather short NN distances the S=C–N–H moiety is non-planar. Dihedral angles as small as 160° are found. The NH chemical shift coefficients measured in non-polar solvents in all the N-substituted-3-piperidinethiopropionamides are more negative (−8 to −17 ppb/K) than in non-hydrogen bonded thioamides. For the latter in non-polar solvents like CDCl₃ and toluene the temperature coefficients are as small as −1 to −4 ppb/K. The large negative effects can be related not only to the non-planarity of the thioamide group in a way that the more pronounced the non-planarity the more negative the temperature coefficients, but also to strong hydrogen bonding and the fact that the acceptor is a nitrogen. For similar amides with non-planar amide groups and nitrogen acceptor large negative temperature coefficients are likewise seen. In polar solvents like DMF the effects in simple thioamides are uniform and close to −6 ppb/K, whereas in the more complex compound like 4p(t) the temperature coefficient is close to 0. An essential feature of measuring temperature coefficients of compounds without strong intramolecular hydrogen bonds in non-polar solvents and at low temperatures is to keep the concentration low enough to avoid dimerisation.     

Novel,organosoluble, light‐colored fluorinated polyimides based on 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl or 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl

Two series of fluorinated polyimides were prepared from 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl ( 2 ) and 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl ( 4 ) with various aromatic dianhydrides via a conventional, two‐step procedure that included a ring‐opening polyaddition to give poly(amic acid)s, followed by chemical or thermal cyclodehydration. The inherent viscosities of the polyimides ranged from 0.54 to 0.73 and 0.19 to 0.36 dL/g, respectively. All the fluorinated polyimides were soluble in many polar organic solvents, such as N,N‐dimethylacetamide and N‐methylpyrrolidone, and afforded transparent and light‐colored films via solution‐casting. These polyimides showed glass‐transition temperatures in the ranges of 222–280 and 257–351 °C by DSC, softening temperatures in the range of 264–301 °C by thermomechanical analysis, and a decomposition temperature for 10% weight loss above 520 °C both in nitrogen and air atmospheres. The polyimides had low moisture absorptions of 0.23–0.58%, low dielectric constants of 2.84–3.61 at 10 kHz, and an ultraviolet–visible absorption cutoff wavelength at 351–434 nm. Copolyimides derived from the same dianhydrides with an equimolar mixture of 4,4′‐oxydianiline and diamine 2 or 4 were also prepared and characterized. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2416–2431, 2004     

Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length

Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (E_a) of the segmental chain motion was lowest for dimeric maltose (E_a = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (E_a = 60.8 ± 1.8 kJ/mol). Subsequently, E_a leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the E_a dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher E_a values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004     

Synthesis and characterization of soluble polyimides containing trifluoromethyl groups in their backbone

A series of polyimides were synthesized from 2,2‐Bis(3,4‐dicarboxyphenyl)hexafluoropropane, 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane, and 4,4′‐oxydianiline by chemical imidization. The effects of the diamine ratios on the properties of the films were evaluated through the study of their thermal, electrical, and morphological properties. All the polymers exhibited better solubility in most of the organic solvents and hence were easily processable. Polyimides with more 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane exhibited better solubility and a low refractive index, which is highly desired for microelectronic applications. The dielectric constant and birefringence were strongly dependent on the fluorine content. With an increase in the fluorine substitution, both the dielectric constant and birefringence decreased. All the polymers exhibited high thermal stability (>400 °C). The absence of crystalline melting in differential scanning calorimetry and broad wide‐angle X‐ray diffraction patterns revealed the amorphous nature of the polymers, which was due to the presence of bulky CF₃ groups and hinged ether linkages of the diamine component. The residual stress values decreased with an increase in the 4,4′‐oxydianiline content, and the results were in agreement with the dielectric constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4303–4312, 2004